Thread: Need help on the steps to solving problem

I have this problem:

4/21=(3p-4)/7sqrt(p^2+20)

I could use a detail step through process for solving this. I know that p=4 or -44/65
I know that it comes downs to using the quadratic formula or factoring to solve the quadratic equation.

my steps so far have been

if 4/21=(3p-4)/7sqrt(p^2+20) then 4/21*7sqrt(p^2+20)=3p-4
next I get 28sqrt(p^2+20)/21=3p-4
then 4sqrt(p^2+20)/3=3p-4
then I multiple both sides be the LCD (3) to eliminate the fraction
I get 4sqrt(p^2+20)=9p-12)
then I need help from here so I fully understand
I know I need to square both sides and factor but I need to know all the steps
thank you!

since you have tried pretty well, here are the steps:

$\displaystyle 4 \sqrt{p^2 + 20} = 9p-12$

squaring both sides

$\displaystyle 16 (p^2 + 20)= {(9p-12)}^2 $

$\displaystyle 16p^2 +320 = 81p^2 - 216 p +144$

$\displaystyle 16 p^2 - 81p^2 +216p +320-144=0$

$\displaystyle -65p^2 +216p +176=0$

$\displaystyle 65p^2-216p-176=0$

can you take from here?

I can take it from there is I use the quadratic formula :

p=-b + or - sqrt b^2-4ac/2a

could you though explain how to factor it properly?

If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44

Originally Posted by colorado

I can take it from there is I use the quadratic formula :

p=-b + or - sqrt b^2-4ac/2a

could you though explain how to factor it properly?

If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44

It's $\displaystyle p = \frac{-b-\sqrt{b^2 -4ac}}{2a}$ or $\displaystyle p = \frac{-b+\sqrt{b^2 -4ac}}{2a}$.
Plugging in values for $\displaystyle a, b $and $\displaystyle c$, you'll get:
$\displaystyle p = 4$ or $\displaystyle p = -44/65$

thanks guys